On a Two Weights Estimate for the Commutator

Abstract

Abstract. We provide quantitative two weight estimates for the commutator of the Hilbert transform under certain conditions on a pair of weights (u, v) and b in Carlu,v. In [10] and [11], Bloom's inequality is shown in a modern setting, and the boundedness of the commutators is provided by assuming both weights u, v are A 2 and b ∈ BM Oρ. In the present paper we show that the condition on b can be replaced by Carlu,v by using the joint A d 2 condition.